Function generator



United States Patent 2 Claims. ci. 235-197 ABSTRACT OF THE DISCLOSURE Afunction generator constructed so that X- and Y-coordinates ofrespective break-points of a function form to be formed by a pluralityof linear segments are first established; then a signal resulting fromsuperimposition of an oscillation waveform on a constant direct currentis generated so as to calculate out a signal corresponding to an outputof a function generator, in case the input signal and the function formof the linear segment approximation function generator are accuratelyestablished from the above-mentioned X and Y-coordinates, and the breakpoint and slope of the linear segment in the abovementioned functiongenerator are adjusted in such a man ner that the difference between theabove calculated signal and the actual output signal of the functiongenerator corresponding to the above-mentioned input signal becomeszero.

This invention relates to apparatuses such as analog computers, and moreparticularly to a new and improved function generator having highlyadvantageous for use in the said apparatuses.

The function generator of this invention is constructed of the followingcomponents so as to attain the intended purpose, i.e., a linear segmentapproximation function generator, voltage dividers to produce electricalsignals which are proportional to the X- and Y-coordinates of the breakpoints of the function form formed by a plurality of linear segments, asetting device to set the dividing ratios of said voltage dividers inaccordance with the function form, a signal generator to generate asignal resulting from superimposition of an oscillation waveform on aconstant direct current, an additional circuit to add the output of saidsignal generator to said electrical signal to be proportional to theX-coordinate and to apply an additional output resultingfrom thisaddition to said function generator, an operational circuit to calculatean additional signal resulting from an addition of said Y-coordinate,and the product of the output of said signal generator, and the slope ofsaid linear segment, a subtractor to obtain the difference signalbetween the output of said function generator and the output of saidoperational circuit, and adjusting means to adjust the break points andslopes of the linear segments in said function generator in order tocause said difference signal to become zero. Furthermore, according tothe invention, when the above adjusting means is made by automaticoperation-s, it is constructed of the following components: a firstservo-mechanism to adjust the break points of the linear segments inorder to cause the D-C component of the output of the subtractortobecome zero, a second servomechanism to adjust the slopes of thelinear segments in order to cause the A-C component of the output of thesubtractor to become zero, first clutch means to couple thepotentiometers of said function generator for adjusting said break pointto said first servomechanism and a second clutch means to couple thepotentiometer of said function generator for adjusting said slopes tosaid second servomechanism.

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The nature, principles, and details of the invention, as Well as itsspecific objects, will be best understood by reference to the followingdescription, taken in conjunction with the accompanying drawings inwhich like parts are designated by like reference characters, and inwhich:

FIGS. 1 and 2 are schematic diagrams indicating the prinicples of twoexamples of diode function generators;

FIG. 3 is a graphical representation indicating the input-outputcharacteristic of a diode function generator such as those shown inFIGS. 1 and 2;

FIG. 4 is a block diagram indicating the composition and arrangement ofa preferred embodiment of the function generator according to theinvention;

FIG. 5 is a fragmentary diagram indicating the details of one part ofthe function generator shown in FIG. 4;

FIG. 6 is a graphical representation indicating a function form to beset and the input-output characteristic for setting;

FIG. 7 is a block diagram indicating automatic function form settingoperation and means; and

FIG. 8 is a fragmentary diagram indicating a modification of one part ofthe arrangement shown in FIG. 5.

For facility in understanding the specific nature and utility of thepresent invention, particularly with respect to its analytical aspects,the following brief consideration of function generators in general andproblems encountered in their design is believed to be necessary.

In an analog computer, in general, a device to generate a voltage whichis an arbitrary function 1 ((2,) with respect to an input voltage 12,,that is, a function generator, is used. Various types of functiongenerators have been proposed and developed. Of these, the functiongenerator of linear segment approximation type which utilizes thenon-linear characteristic of a diode is simple and is widely used.Examples of this type of function generator are shown in FIGS. 1 and 2.

In each of FIGS. 1 and 2, an input 2 is applied to an input terminal Aof a circuit which comprises, essentially, voltage dividers Q Q forbiasing, input resistances R ,R and R ,R diodes D D potentiometers P Pfor controlling the slopes of segments, a high-gain operationalamplifier O, a feedback resistance Rf, and an output terminal B at whichan output voltage 2 is produced.

When the block I enclosed by the dotted line in each of these circuitsis considered in the case when the diode D does not exist, and thedividing ratios of the potentiometers P and Q, are respectively denotedby A and the output produced (straight line including the dotted line inFIG. 3) may be represented by the following equations.

In the case of the circuit shown in FIG. 1,

However, since the diode D exists, an output is produced only in thecase when the terms on the righthand sides of the above Equations 1 and1' are positive. In the case when these terms are negative, the outputbecomes zero because of the rectifying characteristic of the diode, andthe characteristic becomes that as indicated by the full line in FIG. 3.In either case, variation of the dividing ratio of the potentiometer Pcauses the slope 0 of the straight line to vary, and variation of thedividing ratio of the potentiometer Q causes parallel shifting of thestraight line in the horizontal direction.

In each circuit, blocks 1, II, N, each having the operationalcharacteristic as described above, are provided, and a function formwhich results from the summation of the segments produced by theseblocks is obtained from the output terminal B. However, a function formis determined, for example, by the X-coordinates and Y-coordinates ofseveral break points, and suitable adjustment of the positions of saidpoints so as to set a given function form requires a considerable amountof tedious labor.

It is an object of the present invention to provide a function generatorwhereby it is possible to carry out such setting operation in a simplemanner.

It is a further object of the invention to provide a function generatorwherein, through the use of a device to select one predeterminedpotentiometer from among several potentiometers and a device to setautomatically the dividing ratios of potentiometers, function settingcan be carried out fully automatically if the positions of therespective break points are indicated by means such as pushbuttons orpunched tape.

The nature and details of the invention will be further apparent fromthe following detailed description of a preferred embodiment thereof asshown in FIG. 4. In the function generator illustrated in FIG. 4, thereis provided an oscillator 1 (sine wave or rectangular wave) producing anoscillatory Wave (as one example: b sin wt) superimposed on a constantdirect-current component a (where b a). The function form to begenerated is electrically read by a setting device 6 which operates toset the dividing ratios of voltage dividers 2, 2', 3, and 3 inaccordance with the function form so read. The voltage dividers 2, 2',3, and 3' produce electrical signals which are proportional to the X andY coordinates of the break point of the function form to be set, and thesetting operation is accomplished by means such as a relay circuit whichoperates according to instruction read from a punch tape or by meanssuch as a push-button. A device for carrying out such setting operationshas been described, e.g., in Analog Computation, Vol. 1, 1961, pp.83-85, by Stanley Fifer, Ph. D., McGraw-Hill Book Company, Inc.

The output signal (a+b sin wt) of the aforesaid oscillator 1 and theoutput at, of the voltage divider 2 are added by an additional circuit4, and an additional circuit 4' receives as an input the outputs x y nand y of the aforementioned voltage dividers and the output (a-i-b sinwt) of the oscillator 1 and produces as an output a signal which is Oneexample of this additional circuit 4' is shown in FIG. 5. Therein, thereference numerals 8-11 denote the voltage dividers whose dividing ratiois set by the abovementioned setting device 6 so as to generateelectrical signals which are proportional to X- and Y-coordinates of thebreak point of the function form to be set. That is, in this case, theabove-mentioned voltage dividers 8 through 11 are further provided, inaddition to the voltage dividers 2 and 2 as in the above-described FIG.4, and the voltage dividers 9 and 11 are disposed in parallel with thevoltage dividers 2 and 2 by the setting device 6. The voltage dividers 3and 3' are not particularly necessary to be provided, since the voltagedividers 8 and 10 are provided. It goes without saying that the voltagedividers 2, 2, 3 and 3' arranged as shown in FIG. 4 may becomenecessary, if and when other circuit construction than that shown inFIG. is adopted. This is merely a problem in circuit designing and caneasily be done by skilled artisans as a case necessitates, hence it hasno direct pertinence to the essential subject matter of the invention.The reference numeral 12 shows an operational amplifier, 13 is an adder,and 14 and 15 are sign changers.

Now, assume that the gain of the operational amplifier 12 issufficiently large (this is a condition which is always established inan operational amplifier. See the abovementioned literature, ifnecessary), and there is a relationship of x x, In this case, the outputs of the operational amplifier takes a value to render the summation ofthe input to be zero, and the amplifier becomes stable, as representedby the following equation.

( -l- Sin (yi)i+1) o( 1 1 i+1)= Z/iyi+1 e -(a+b sin wt) Accordingly, atthe terminal of the adder 13, an output having the value represented bythe following equation can be obtained.

e0+yi=y.+( sin 0 i+1 m In the case of relationship of x,+ x, 0, thedividing ratio of the voltage divider 10 is set at x, and of the voltagedivider 11 at 36 1. Also when x x 0, the dividing ratios of the voltagedividers can be same as those of the case of x x,+ 0, although theabsolute values of x and x may simply be established. (In the literatureAnalog Computation, vol. II, 1961, McGraW-Hill Book Company, Inc., pages833-838, there is described a technical discussion similar to theabove-mentioned matter.) In this case, by using this circuit in actualpractice, the addition (y e can be carried by utilizing the amplifier ofthe succeeding stage without particularly providing the aforementionedadder 13. Furthermore, a term such as y, y can also be obtained by meansof a resistance network as is shown in FIG. 8. In this figure, aresistor 16 is connected at its both ends together in a ring shape (thetotal resistance value thereof is assumed to be 1). Now, this resistor16 is cut at an appropriate position distant by y from the standardposition 0, the one end of the cut portion 17 being applied with aninput e,, and the other being grounded, so that an output may be takenout from this y position distant from the abovementioned standardposition. In this manner, it is possible to obtain an output of e (y ysince the resistance value from the input e, to the grounded point is 1and that from the output point to the grounded point is y, y It will beclear that this type of the resistor 16 can be used in place of thevoltage dividers and the sign changers as shown in FIG. 5.

Referring again to FIG. 4, the output signals (x -l-a-l-b sin wt), ofthe circuit 4 is applied to a function generator 5 such as thatindicated in FIG. 1 or FIG. 2. The output e of the function generator 5and the output yi+1 yi (y,+(a+b sin wt)xi+l xi of the additional circuit4 are led to a subtractor 7, by which a signal E which is the differenceof the two said outputs is obtained. If, in the function generator 5,the outputs of the potentiometers Q Q Q for respective biasing withinthe blocks 1, II, N are caused to assume amply large negative values sothat the diodes D D D will not be conductive within the range of theinput signal (or if the input is cut off from the amplifier 0); nooutput will be produced by the function generator 5. When the diode Dalone is rendered conductive and two coordinates (x 3 and x y are set inthe voltage dividers 2, 2, 3 and 3' (in the case of using theoperational circuit shown in FIG. 5, the voltage dividers 2, 2 and 8through 11 are used), an oscillation waveform expressable as (x -l-a-l-bsin wt) enters the function generator 5, and another oscillationwaveform exprcssable as is produced by the operational amplifier 4 (X+a+b sin wt) y (a+b sin :022:

is equal to the output of block I of the function generator 5 in thecase when (X +a+b sin wt) is introduced into the function generator 5,the block I of which is correctly set. Accordingly, when thepotentiometers P and Q in the function generator 5 are set so as not tocause differences between the output of the operational circuit 4 andthe output of the fusction generator 5, the function form (linearsegment) between the first break point (X Y and the second break poing(X Y is correctly set. (This difference is the output E of thesubtractor 7. This subtractor 7 has been known conventionally, and isgenerally represented in the form of a circuit to sum up both positiveasd negative inputs as shown in the aforementioned literature AnalogComputation, vol. 1, page 162.)

In order to cause the said difference to be zero, the potentiometer P,for slope is so adjusted that the alternating-current component of thedifference output becomes zero, and the potentiometer Q for biasing isso adjusted that the direct-current component becomes zero. Uponcompletion of these adjustments, in order to carry out the succeedingsetting, x y and x 3 are set in the voltage dividers 2, 2' and 3, 3, andthe same adjustment procedure is followed with the potentiometers P andQ of the function generator. This procedure is repeated to the finalbreak point, N, whereupon the desired function form is set.

The foregoing description indicates the principle of the invention. Inan actual apparatus, a sign changer for causingthe slope to becomenegative and a circuit without diodes for only bias for causing theentire function form to move up and down in the y direction becomenecessary. Furthermore, it becomes necessary to provide means to causethe value of a or the value of b to be variable in accordance with thefunction form to be set. Thus, a number of auxiliary facilities becomesnecessary. In the case wherein the setting of the potentiometers P P Pand Q Q Q is to be carried out manually, such a method as applying theoutput of the subtractor 7, for example, to the Y-axis of a cathode-raytube and carrying out the operation by oscillating the X-axis thereofwith sin wt while observing the resulting pattern may be adopted.However, in the case wherein these potentiometers P P P and Q Q Q areset by automatic setting means such as servo-mechanisms, it is possibleto set the function form in a fully automatic manner by providingautomatic setting of potentiometers and providing indication of the xand y coordinates of the break point through the use of push buttons,the reading of a punch tape or a punch card, or the output from adigital computer.

An example of setting by means of a punch tape is indicated in FIG. 7. Atape reader 6 reads the values of break point coordinates x y r 3 andsets the same by means of relay circuits in voltage dividers 2, 2', 3,and 3' in the case of using the operational circuit shown in FIG. 5, thevoltage dividers 2, 2' and 811 and potentiometers P and Q, (i=1, 2, N)are coupled to the output shafts of servomotors T and T by clutches cand v The servomotor T' of the potentiometer Q, is driven by the DCcomponent taken out by a filter F from the output E of the subtractor 7,and the servomotor T of the potentiometer P is driven by the powerresulting from synchronous rectification by a rectifier circuit R of theA-C component of the output of the subtractor 7. These servomechanismsadjust the dividing ratio of the abovementioned potentiometers P and Qso as to cause the AC. and D.C. components of the output of subtractor 7to become zero. Then, after a certain predetermined time, or when boththe A-C component and D-C component of the output of the subtractor 7become less than a certain value, the clutches c and 0, shift to thesucceeding operation, and the tape reader 6 reads the values of thesucceeding break point and carries out the succeeding setting. Theoperation proceeds in this manner until the final setting isaccomplished.

Since, after setting of x 31,, x and y in the voltage dividers 2, 2', 3,and 3' and completion of the setting of the potentiometers, x, 3 x and yare next set, it is convenient to use the voltage dividers 2, 2', 3, and3' by alternately switching the outputs of 2, 2' and 3, 3'.

In the'case wherein a large number of function generators according tothe present invention are used in combination, since a large part of theapparatus can be used commonly for all of the said function generators,the present invention is particularly applicable to cases such as thatwherein it is desired to include a large number of function generatorsin a single computer.

It should be understood, of course, that the foregoing disclosurerelates to only a preferred embodiment of the invention and that it isintended to cover all changes and modifications of the example of theinvention herein chosen for the purposes of the disclosure, which do notconstitute departures from the spirit and scope of the invention as setforth in the appended claims.

What is claimed is:

1. A function generator comprising: a linear segment approximationfunction generator; voltage dividers to produce electrical signals whichare proportional to the X- and Y-coordinates of the break points of thefunction form formed by a plurality of linear segments; a setting deviceto set the dividing ratios of said voltage dividers in accordance withthe function form; a signal generator to generate a signal resultingfrom superimposition of an oscillation waveform on a constant directcurrent; an additional circuit to add the output of said signalgenerator to said electrical signal to be proportional to theX-coordinate and to apply an additional output resulting from thisaddition to said function generator; an operational circuit to calculatean additional signal resulting from addition of said Y-coordinate, andthe product of the output of said signal generator and the slope of saidlinear segment; a subtractor to obtain the difference signal between theoutput of said function generator and the output of said operationalcircuit; and an adjusting means to adjust the break points and slopes ofthe linear segments in said function generator in order to cause saiddifference signal to become zero.

2. The function generator according to claim 1, wherein said adjustingmeans is constructed by a first servomechanism to adjust the breakpoints of the linear segments in order to cause the DC. component of theout put of the subtractor to become zero; a second servomechanism toadjust the slopes of the linear segments in order to cause the AC.component of the output of the subtractor to become zero; a first clutchmeans to couple potentiometers of said function generator for adjustingsaid break point to said first servomechanism and a second clutch meansto couple potentiometers of said function generator for adjusting saidslopes to said second servomechanism.

References Cited

1. A FUNCTION GENERATOR COMPRISING: A LINEAR SEGMENT APPROXIMATIONFUNCTION GENERATOR; VOLTAGE DIVIDERS TO PRODUCE ELECTRICAL SIGNALS WHICHARE PROPORTIONAL TO THE XAND Y-COORDINATES OF THE BREAK POINTS OF THEFUNCTION FORM FORMED BY A PLURALITY OF LINEAR SEGMENTS; A SETTING DEVICETO SET THE DIVIDING RATIOS OF SAID VOLTAGE DIVIDERS IN ACCORDANCE WITHTHE FUNCTION FORM; A SIGNAL GENERATOIR TO GENERATE A SIGNAL RESULTINGFROM SUPERIMPOSITION OF AN OSCILLATION WAVEFORM ON A CONSTANT DIRECTCURRENT; AN ADDITIONAL CIRCUIT TO ADD THE OUTPUT OF SAID SIGNALGENERATOR TO SAID ELECTRICAL SIGNAL TO BE PROPORTIONAL TO THEX-COORDINATE AND TO APPLY AN ADDITIONAL OUTPUT RESULTING FROM THISADDITION TO SAID FUNCTION GENERATOR; AN OPERATIONAL CIRCUIT TO CALCULATEAN ADDITIONAL SIGNAL RESULTING FROM ADDITION OF SAID Y-COORDINATE, ANDTHE PRODUCT OF THE OUTPUT OF SAID SIGNAL GENERATOR AND THE SLOPE OF SAIDLINEAR SEGMENT; A SUBTRACTOR TO OBTAIN THE DIFFERENCE SIGNAL BETWEEN THEOUTPUT OF SAID FUNCTION GENERATOR AND THE OUTPUT OF SAID OPERATIONALCIRCUIT; AND AN ADJUSTING MEANS TO ADJUST THE BREAK POINTS AND SLOPES OFTHE LINEAR SEGMENTS IN SAID FUNCTION GENERATOR IN ORDER TO CAUSE SAIDDIFFERENCE SIGNAL TO BECOME ZERO.